Blockchain is not just a decentralised database, but it is much more than that. While the original Bitcoin blockchain allowed only value to be transferred, along with limited data with every transaction, several new blockchains have been developed in the past 2-3 years, which have much more advanced native scripting and programming capabilities.
Apart from the Bitcoin blockchain, I would say that there a few other major blockchains like Ethereum, Ripple, R3's Corda, Hyperledger. Although Ethereum has a crypto-currency called Ether, it is actually a Turing complete EVM (Ethereum Virtual Machine). Using Ethereum, you can create Smart Contracts that would themselves run in a decentralised manner. As a developer, it opens up completely new avenues for you and changes your perspective of writing programs. While Ripple is mainly geared towards payments, Corda and Hyperledger are built with a view of being private/permissioned blockchains, to solve the issues such as scalability, privacy, and identity. The target markets for Hyperledger and Corda are mostly banks and other Financial Institutions.
As for the non-bitcoin application of blockchain, you can certainly look at some companies like Consensys (multiple different use cases on blockchain), Digix Global (gold tokens on the blockchain), Everledger (tracking of diamonds on the blockchain), Otonomos (Company registration on the blockchain), OT Docs (Trade Finance and document versioning on the blockchain) amongst others.